#4, it could also raise questions if OP leaves Schengen zone on his Australian passport and then reenters on his Polish passport. On his reentry the SIS system may show him as he had never left the EU - so how on earth is he entering instead of leaving? I guess however most border guards would just wave him through.
#5 - you can easily travel across the EU on the new Polish passport, as on travelling through Schengen Europe (EU minus UK, Ireland, Bulgaria, Romania and Cyprus) you either won't be controlled at all or would be only asked to show your passport on assumption that you started your trip in Poland. The problem is only what you should show on the EU external border, i.e. on leaving the Schengen zone. I would rather advise to show your Polish passport but Ruth has a different view.
BTW - even if you don't show the Australian passport on leaving and the Schengen information system shows you as having overstayed (based on Australian passport record), it should have no consequences for you, because as a Polish citizen you will have a legal right to enter and reside in the EU regardless of your previous visa history, including any entries in the SIS system.